## A Concise Introduction to Pure Mathematics, Second EditionA Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems. The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics. What's New in the Second Edition: The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preface jd 1 Sets and Proofs | 1 |

Number Systems | 13 |

Decimals | 21 |

Inequalities | 27 |

n1 Roots and Rational Powers | 31 |

Complex Numbers | 35 |

Polynomial Equations | 47 |

Induction | 57 |

Congruence of Integers | 111 |

More on Congruence | 121 |

Secret Codes | 131 |

Counting and Choosing | 137 |

More on Sets | 149 |

Equivalence Relations | 157 |

Functions | 163 |

Permutations | 173 |

Eulers Formula and Platonic Solids | 71 |

Introduction to Analysis | 81 |

The Integers | 91 |

Prime Factorization | 99 |

More on Prime Numbers | 107 |

Infinity | 187 |

Further Reading | 197 |

199 | |

201 | |

### Other editions - View all

### Common terms and phrases

2-cycle Algebra answer bijection called Cartesian product choose codes coefficients complex numbers congruence equation connected plane graph contradiction coprime countable critic Ivor Smallbrain cube roots cubic equation cycle notation cycle-shape decimal expressions deduce define DEFINITION Let digits divides divisible edges elements equal equivalence classes equivalence relation Euclidean algorithm Euler's formula example Exercises for Chapter Fermat's Little Theorem finite sets function Fundamental Theorem Hence inequality infinite set integers s,t Liebeck lower bound Mathematical Induction mathematics method Miller's test modulo multiple n'h roots number system odd permutations pairs pigeonhole Platonic solids polyhedron positive integer positive real number prime factorization prime numbers product of prime PROOF Let prove rational number real line real number remainder result root of unity sends sequence set consisting solution solve subsets Suppose symbol tions total number true upper bound vertex vertices words write

### Popular passages

Page iv - TK5103.452.P75 2006 621.382'7-dc22 2005051485 informa Taylor & Francis Group is the Academic Division of Informa pie. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com...